# Calculate the Number of Periods in Repeated Percentage Change

In this worksheet, students will work out the number of periods required to find a repeated percentage change.

Key stage:  KS 3

Curriculum topic:   Number

Curriculum subtopic:   Interpret Fractions/Percentages as Operators

Difficulty level:

#### Worksheet Overview

This activity is about finding a required period of time when given a repeated percentage change.

You will need a calculator for this activity!

Recap

We know that if we invest £3,000 in the bank for 4 years at an interest rate of 3%, to find the total amount after 4 years we would do the calculation:

# £3,000 x 1.034

£3,000 being the investment

1.03 being the multiplier for an increase of 3%

The power 4 being the 4 (periods) years we need to calculate.

We also know if a car cost £5,000 and it depreciated by 2% every year, to find the value of the car after 5 years we would do the calculation:

# £5,000 x 0.985

£5,000 being the initial cost of the car

0.98 being the multiplier for an decrease of 2% (100 - 2 = 98)

The power 5 being the 5 (periods) years we need to calculate.

In this activity, we will be given all the information, but we will have to find the number of periods/years/the power.

If you are confused, a look at a typical question will help.

Example

Mr Penny invested £4,000 in the bank at an interest rate of 6%.

He wanted to leave it in there until his investment was worth more than £5,000

For how many years would Mr Penny have to leave his money in the bank?

We use the same formula as in the recap:

# 4,000 x 1.06n > 5,000

£4,000 the investment

1.06 being the multiplier for an increase of 6%

The power is unknown as we don't know how long it will take, so we write n

We do know that we need the total to be > £5,000

When we have the formula, we use trial and improvement to find n!

Let's try n = 1 year first

# 4,000 x 1.061 = 4,240 (not > 5,000)

Let's try n = 2 years

# 4,000 x 1.062 = 4,494.40 (not > 5,000)

Let's try n = 3 years

# 4,000 x 1.063 = 4,764.06 (not > 5,000)

Getting nearer!

Let's try n = 4 years

# 4,000 x 1.064 = 5,049.91 (this is > 5,000)

Therefore, Mr Penny would need to leave his money in the bank for 4 years to get more than £5,000

Tip: If it is taking a long time to get anywhere near the amount you need, you can skip some to get there quicker!

Let's try some of these!

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